I am one of those who said to move on but..... Ask yourself this.
If she said tomorrow she wants to come back, would you let her right back into your home? If she broke up with OM, would she have anywhere else to go with her kids?
Don't take her back so quickly and for the wrong reasons if she does.
If she said tomorrow she wants to come back, would you let her right back into your home? Yes I would. Number one, that is what I desire, no matter how illogical. Two, from a DB perspective it would mean that by me doing something different I got a different result. Three, legally it is still her place of residence, she has keys, I can't legally change the locks, and she has to either officially get her mail sent somewhere else or I have to legally evict her.
If she broke up with OM, would she have anywhere else to go with her kids? She has stayed at her Nans, dads, friends, etc without problem. I believe that if they cut it off and she didn't want to be at the house she wouldn't. Even if she had no other place to go she would avoid me like the plague if she so felt that way...meaning I'd still basically never see her even when home.
If you accept her back for the wrong reasons without real work done on her part, you will end up right back where you started. "It takes one to tango."
“People are just as happy as they make up their minds to be.” Abraham Lincoln
